New method selects diffusion scales for graph wavelets.
problem Choosing optimal diffusion scales for graph wavelets.
method Proposes an unsupervised method using information theory.
result Method selects diffusion scales for graph wavelets.
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48 results for “diffusion scales”
The abstract explores connections between reinforcement learning, scaling, and diffusion.
problem Aligning reinforcement learning with human feedback and scaling techniques.
method Clarifying connections between reinforcement learning, scaling, and diffusion.
result Introducing a resampling approach for alignment and reward-directed diffusion models.
New method improves robustness of large models without sacrificing accuracy.
problem Improving robustness of large pre-trained models without accuracy loss.
method Multi-scale diffusion denoised smoothing, selectively applying smoothing at multiple noise scales.
result Strong certified robustness at high noise levels with accuracy close to non-smoothed classifiers.
Residual Prior Diffusion integrates coarse latent priors with diffusion models for better generative tasks.
problem Diffusion models struggle with representing both large-scale and fine-scale details in data distributions.
method Two-stage framework: first a coarse prior model captures large-scale structure, then a diffusion model represents the residual.
result RPD accurately captures fine-scale details while preserving large-scale structure, outperforming standard diffusion models.
Pixel-space diffusion models outperform latent models on high-resolution image synthesis.
problem Efficiency and quality trade-off in high-resolution image synthesis.
method Sigmoid loss-weighting, simplified architecture, and resolution scaling.
result Achieved 1.5 FID on ImageNet512, new SOTA results on other datasets.
Improves diffusion model performance and efficiency through classical search.
problem Tackles inference-time control in diffusion models.
method Proposes a framework combining local and global search for efficient navigation.
result Significant gains in performance and efficiency across various domains.
Remasking improves the quality of discrete diffusion models for natural language and image generation.
problem Limited iterative refinement in masked discrete diffusion models.
method Introducing ReMDM sampler that allows remasking during inference.
result Remasking enables better quality outputs with increased sampling steps.
Denoising Diffusions with Optimal Transport: Localization, Curvature, and Multi-Scale Complexitystat.ML
This paper tackles denoising of complex measures using optimal transport and curvature analysis.
problem Denoising of complex, possibly non-log-concave measures.
method Score function and optimal transport theory to revert Langevin diffusion chains.
result The difficulty of denoising depends on the curvature complexity of the initial measure at specific SNR scales.
Soft Truncation improves diffusion model performance by balancing loss scales across diffusion times.
problem Inverse correlation between density estimation and sample generation in diffusion models.
method Introduces Soft Truncation, a training technique that softens the truncation hyperparameter.
result Soft Truncation achieves state-of-the-art performance on various datasets.
New method reduces memorization in diffusion models without sacrificing image quality.
problem Diffusion models often memorize training data, especially with small datasets.
method Train models using noisy data at large noise scales to reduce memorization.
result Significant reduction in memorization without compromising image quality.
New algorithm clusters hyperspectral images at multiple scales.
problem Clustering hyperspectral images at various scales.
method M-SRDL algorithm using spectral-spatial diffusion distances.
result More accurate clustering labels achieved with spatial regularization.
Study on curve diffusion flows with scale-critical curvature term.
problem Analyzing stability of curve diffusion flows with scale-critical curvature.
method Introduced and studied a one-parameter family of curve diffusion flows with a scale-critical cubic curvature term. Analyzed dynamical stability of homothetic circles using variational methods.
result Established that any small perturbation of an -fold circle monotonically approaches the unit -circle after rescaling, translation, and reparametrisation.
A new pyramidal diffusion model speeds up image generation.
problem Training and evaluating diffusion models are time-consuming.
method Introduces a pyramidal diffusion model with a single score function.
result Generates high-resolution images from low-resolution starting points efficiently.
Unified continuous diffusion model outperforms discrete alternatives in scalability and quality.
problem Continuous diffusion models were perceived as less scalable than discrete models.
method Reconstructed Plaid model and compared it with modern discrete DLMs, optimizing noise schedule and embeddings via likelihood.
result Unified continuous diffusion model (RePlaid) outperforms discrete models in compute efficiency and quality.
DriftLite improves inference quality of diffusion models without retraining.
problem Adapting pre-trained diffusion models to new target distributions without retraining.
method Lightweight, training-free particle-based approach that steers inference dynamics with optimal stability control.
result Consistently reduces variance and improves sample quality over existing methods.
MELD model clusters data at multiple scales, improving understanding of latent structure.
problem Understanding latent multiscale structure in datasets.
method Multiscale Learning by Unsupervised Nonlinear Diffusion (M-LUND) algorithm.
result M-LUND detects latent structure in synthetic and real datasets.
This paper improves generative models by using data scaling and theoretical analysis.
problem Challenges in selecting noise distributions for stable learning in generative models.
method Introduces Scale-GAN, which uses data scaling and variance-based regularization.
result Data scaling controls the bias-variance trade-off and improves stability and accuracy.
Based on the new type of random walk process called the Potentials of Unbalanced Complex Kinetics (PUCK) model, we theoretically show that the price diffusion in large scales is amplified 2/(2 + b) times, where b is the coefficient of quadratic term of the potential. In short time scales the price diffusion depends on …
Paper investigates separating times for general diffusions, providing new insights.
problem Understanding phase transitions between equivalence and singularity in diffusions.
method Representation of separating time as hitting time of a deterministic set, characterized by speed and scale.
result Explicit and easy-to-check conditions for absolute continuity and singularity of diffusions.
The financial market is nonpredictable, as according to the Bachelier, the mathematical expectation of the speculator is zero. Nevertheless, we observe in the price fluctuations the two distinct scales, short and long time. Behaviour of a market in long terms, such as year intervals, is different from that in short ter…
Improved diffusion models for manifold learning.
problem Learning distributions on general manifolds with geometric complexity.
method Revised approximations for score matching on symmetric spaces.
result Improved performance and scalability to high dimensions.
ISB learns nonlinear diffusion processes between images.
problem Image restoration tasks, especially with limited structural information.
method Conditional diffusion models, Schrödinger bridge approach.
result ISB outperforms standard models in various image restoration tasks.
A hybrid model combines diffusion and neural operator methods for stress prediction in hyperelastic materials.
problem Challenges in predicting stress fields in hyperelastic materials with complex microstructures.
method A hybrid surrogate framework combining a conditional denoising diffusion probabilistic model (cDDPM) and a modified DeepONet.
result The hybrid model consistently outperforms traditional methods by one to two orders of magnitude.
Improved continuous-time consistency models for large-scale image generation.
problem Training instability and discretization errors in existing diffusion models.
method Unified theoretical framework, improved diffusion process, and network architecture.
result Trained continuous-time CMs at 1.5B parameters, achieving state-of-the-art FID scores.
The aim of this paper is to examine the time scaling of the semivariance when returns are modeled by various types of jump-diffusion processes, including stochastic volatility models with jumps in returns and in volatility. In particular, we derive an exact formula for the semivariance when the volatility is kept const…
New model generates images by reversing heat equation, revealing disentanglement.
problem Image generation without considering image structure.
method Stochastically reverses the heat equation to generate images, using variational approximation.
result Emergent disentanglement of overall colour and shape in images.
The Perona-Malik model has been very successful at restoring images from noisy input. In this paper, we reinterpret the Perona-Malik model in the language of Gaussian scale mixtures and derive some extensions of the model. Specifically, we show that the expectation-maximization (EM) algorithm applied to Gaussian scale …
Anomalous diffusion and long-range memory in the scaled voter modelcond-mat.stat-mech
Analyzed a generalized voter model with power-law herding intensity, revealing anomalous diffusion and long-range memory.
problem Anomalous diffusion and long-range memory in a generalized voter model.
method Derived analytical expressions for moments and first passage time distribution, confirmed numerically.
result The model exhibits long-range memory indicators despite being a Markov model.
SFM resolves small-scale physics challenges in weather data.
problem Challenges in super-resolving small-scale details in physical sciences like weather.
method Encoding inputs to a latent base distribution, flow matching for stochastic details, adaptive noise scaling.
result SFM framework significantly outperforms existing methods.
Diffusion Maps meet Nyströmstat.ML
Diffusion maps are an emerging data-driven technique for non-linear dimensionality reduction, which are especially useful for the analysis of coherent structures and nonlinear embeddings of dynamical systems. However, the computational complexity of the diffusion maps algorithm scales with the number of observations. T…
Diffusion models achieve high-quality samples from complex high-dimensional Gaussian mixtures without scaling with dimension.
problem Achieving accurate sampling from high-dimensional distributions using diffusion models.
method Investigates the effectiveness of diffusion models in sampling from Gaussian Mixture Models (GMMs) without scaling with dimension.
result DDPM requires at most iterations to attain an -accurate distribution in total variation distance, independent of dimension and number of components.
Nonstationary Increments, Scaling Distributions, and Variable Diffusion Processes in Financial Marketsphysics.soc-ph
Arguably the most important problem in quantitative finance is to understand the nature of stochastic processes that underlie market dynamics. One aspect of the solution to this problem involves determining characteristics of the distribution of fluctuations in returns. Empirical studies conducted over the last decade …
Localized diffusion models reduce training complexity by exploiting low-dimensional structure.
problem Training diffusion models is computationally expensive due to the curse of dimensionality.
method Localized neural networks and localized score matching loss to estimate low-dimensional score functions.
result Localized diffusion models can circumvent the curse of dimensionality with reduced sample complexity.
Decomposing market impact into diffusive components
problem Market impact scaling
method Decomposing impact into realized and counterfactual returns
result Implication of square-root law in information-neutral regime
This paper proposes and analyzes a novel clustering algorithm that combines graph-based diffusion geometry with techniques based on density and mode estimation. The proposed method is suitable for data generated from mixtures of distributions with densities that are both multimodal and have nonlinear shapes. A crucial …
Early stopping improves generalization in overparameterized diffusion models.
problem Understanding and optimizing generalization in overparameterized diffusion models.
method Revisiting diffusion models, showing generalization occurs before memorization, and developing a phase diagram.
result Generalization time scales with dataset size, supporting early-stopping criteria.
We analyze the probability of ruin for the {\it scaled} classical Cramér-Lundberg (CL) risk process and the corresponding diffusion approximation. The scaling, introduced by Iglehart \cite{I1969} to the actuarial literature, amounts to multiplying the Poisson rate $\la$ by , dividing the claim severity by $\sqrtn$, …
Study no-arbitrage conditions in 1D diffusion markets with interest rates.
problem Determining no-arbitrage conditions in 1D diffusion markets with interest rates.
method Established deterministic criteria for no-arbitrage notions in terms of scale function and speed measure.
result Revealed various effects, e.g., NIP not excluded by reflecting boundaries.
Reaction-Diffusion-Branching Models of Stock Price Fluctuationscond-mat.stat-mech
Several models of stock trading [P. Bak et al, Physica A {\bf 246}, 430 (1997)] are analyzed in analogy with one-dimensional, two-species reaction-diffusion-branching processes. Using heuristic and scaling arguments, we show that the short-time market price variation is subdiffusive with a Hurst exponent . Biase…
SGLDiff approximates Bayesian posterior distributions with subsampling error.
problem Approximating Bayesian posterior distributions in large-scale data settings.
method Stochastic Gradient Langevin Diffusion (SGLDiff) with subsampling.
result The Wasserstein distance between the posterior and SGLDiff's limiting distribution is bounded by a fractional power of the mean waiting time.
SDIFT generates full-field dynamics from sparse, irregular data.
problem Modeling and reconstructing physical dynamics from sparse, off-grid observations.
method SDIFT uses a functional Tucker model and sequential diffusion for generating full-field evolution from irregular sparse observations.
result Significant improvements in reconstruction accuracy and computational efficiency compared to state-of-the-art approaches.
URGE improves diffusion model quality without gradients or Hessian.
problem Improving sample quality in diffusion models without gradient evaluations.
method Path-wise importance reweighting via Girsanov change of measure.
result URGE achieves better generation quality than existing methods.
Improved deep hierarchical VAE with diffusion-based VampPrior.
problem Latent variable generative modeling challenges.
method Hierarchical VAE with amortized diffusion-based VampPrior.
result Better performance with fewer parameters and improved stability.
We study the small-time fluctuations for diffusion processes which are conditioned by their initial and final positions, under the assumptions that the diffusivity has a sub-Riemannian structure and that the drift vector field lies in the span of the sub-Riemannian structure. In the case where the endpoints agree and t…
Markov Processes, Hurst Exponents, and Nonlinear Diffusion Equations with application to financecond-mat.stat-mech
We show by explicit closed form calculations that a Hurst exponent H that is not 1/2 does not necessarily imply long time correlations like those found in fractional Brownian motion. We construct a large set of scaling solutions of Fokker-Planck partial differential equations where H is not 1/2. Thus Markov processes, …
Discrete diffusion models improve text and image inference.
problem Challenges in posterior sampling with discrete diffusion models.
method Anchored Posterior Sampling (APS) with quantized expectation and anchored remasking.
result APS achieves state-of-the-art performance on various tasks.
Analyzed geometric and diffusion properties of a coupled system.
problem Qualitative behavior of a geometric evolution coupled with diffusion.
method Mean curvature flow scaled with diffusion equation analysis.
result Surface area strictly decreases, but solutions can exist infinitely.
This paper simplifies diffusion models for high resolution images.
problem Applying diffusion models to high resolution images is challenging.
method Adjust noise schedule, scale specific parts, add dropout, and use downsampling.
result Achieved state-of-the-art image generation performance.